Question

is (4 7) a solution to the inequality y - 3⁄4 x - 5 true or false

Answer 1

To determine if the point \( (4, 7) \) is a solution to the inequality \( y - \frac{3}{4}x - 5 \), we first need to rewrite the inequality properly. It seems like you've presented it as an expression rather than an inequality. Assuming the intended inequality is:

\[
y - \frac{3}{4}x - 5 > 0
\]

or some similar inequality, let's evaluate it with the point \( (4, 7) \):

1. Substitute \( x = 4 \) and \( y = 7 \) into the expression.

\[
7 - \frac{3}{4}(4) - 5
\]

2. Calculate \( \frac{3}{4}(4) \):

\[
\frac{3}{4} \times 4 = 3
\]

3. Substitute that back into the expression:

\[
7 - 3 - 5
\]

4. Simplify:

\[
7 - 3 = 4
\]
\[
4 - 5 = -1
\]

Now, you have:

\[
-1 > 0 \quad \text{(which is false)}
\]

Thus, the point \( (4, 7) \) does not satisfy the inequality \( y - \frac{3}{4}x - 5 > 0 \).

If the inequality were instead \( y - \frac{3}{4}x - 5 < 0 \), then we would be evaluating \( -1 < 0 \), which would be true.

In conclusion, based on the analysis we've made with the inequality I assumed, \( (4, 7) \) is **false** for \( y - \frac{3}{4}x - 5 > 0 \).